If all you want is all out attack, then dual wield is most appropriate as there is no block feature, I very much like the idea of two war axes, if you want to go two handed, I personally use a battleaxe with my barbarian nord, but that is just personal preference, I just think that battleaxes look quite good.
As far as 2H goes, Waraxes and Greatswords have the same speed.
Now, for DW...The speed is based on the weapon you wield in the left hand. So a brutal damage output would be a Dagger in the left hand and a Mace in the right hand. However, a Sword in the left and a Mace in the right is somewhat of a favored combination for optimum damage output.
Still, twin axes do look cool and sometimes look will trump practicality and efficiency every time.
Why not do both? I have a character with dual axes for lower level enemies and a greatsword for stronger ones.
Brute strength you say? Real brutes would just use their damn fists because they're just that tough